The length of three wires is $$ 75 \mathrm{~m}, 85 \mathrm{~m} $$ and 95 m . Find the length of the rod that can be use to measure exactly.

Question

UpStudy AI · Accepted Answer

We need to find a rod length $$ L $$ such that each wire can be divided completely into rods of length $$ L $$. This means $$ L $$ must be a divisor of all three lengths. To get the longest possible rod length, we find the greatest common divisor (GCD) of the three wire lengths.

1. Express each length:
   - $$75 = 3 \times 5^2$$
   - $$85 = 5 \times 17$$
   - $$95 = 5 \times 19$$

2. The common prime factor among all three numbers is $$5$$.

3. Therefore, the greatest common divisor is:
   $$
   \text{GCD}(75, 85, 95) = 5
   $$

Thus, the length of the rod that can be used to measure exactly is $$5 \, \text{m}$$.
The rod length that can be used to measure exactly is 5 meters.

The length of three wires is and 95 m . Find the length of the rod that can be use
to measure exactly.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions

The length of three wires is and 95 m . Find the length of the rod that can be use to measure exactly.